Round Edges on solidified mesh
Did you try proportional editing mode? If not, that might be worth a shot. Rough outline of how I would go about it:


Bridge the edge loops (works best if both loops have the same number of verts)
Do several loop cuts on the face loop added to create the bridge
Turn on proportional editing mode and set it to "Sphere" or "Smooth"
Select the inner most ring of the loop cuts
Grab and move or scale the selected loop